Create a hexagon pattern
Your question is not clear enough, but if you're talking about a 3D object, here is a way to do it (maybe there's a simpler?):


Create a 6 vertices circle, subdivide it once, extrude it inwards and merge.
Extrude it up on the Z axis.
Extrude a 12 vertices cylinder from one of its face.





Delete 5/6 of the shape so that you only keep 1/6.
Put an empty at the same point as the origin of the object.
Use it as the object of an Array modifier / Object Offset mode, Count = 6.
Rotate the empty 60° on the Z axis so that the shape make a 360° star shape.





Apply the Array modifier. Delete the empty.
Repeat the star shape 7 times, use the Snap option / Vertex mode to make the shapes stick to each others.
Only keep the centre of this shape, it will be your pattern.
Remove any doubles.





Give it an Array modifier / Relative Offset mode, on the X axis. Choose the amount of iterations with the Count value.
Give it a second Array modifier / Relative Offset mode, on the Y axis.